Multiple instances of same image node?
I may have just invalidated the rest of my answer as I realised you can just edit the Source property of an image from the Node Editor's Properties Shelf (N) when you have an image node selected, which will update all image nodes that share that image:



This is because when you duplicate an image node the image is instanced (shared). When you edit the Source property you are editing a property on an existing image, so the other nodes that use that instanced image see the changes. When you normally browse to a new image you break the connection to the other intances so they don't update.

So, you can inform users that changing the Source property in the Properties Shelf on one image will update all the relevant images, or you can look at my original answer, below, for other solutions.





Original Answer

My suggestion would be to group the Image node within a group, with the Vector as input and the Color and Alpha of the image as output:



Whenever you need to use the same image you add the node group instead:



Obviously, this still doesn't usefully expose the image path to the user, but at least they only have to change the one image (because all other image groups will also update). 

You could even place an additional one of these group nodes in a more accessible place in your node tree with instructions that this is where you can change the image (instead of the user having to dig through a particularly complex node tree):



(The description comes from a text file, so this may or may not be suitable for your situation).

An alternative solution is to provide a small script along with your material that has an interface for providing a new path which then updates the node's filepaths.

For example:

newFilepath = "C:\Filepath\To\Image"
bpy.data.materials['MyMaterial'].node_tree.nodes['Image Texture'].image.filepath = newFilepath 


This changes the filepath for the image on the MyMaterial material. 

If you have questions about how to provide an interface for selecting a file and returning a filepath to your script you can either ask a new question (or search this site for Existing Questions).